A Libre Knowledge Page (Rev.16.12.2014)

Tools and standard reports for piping engineers
User developed Excel function, are included in each application
This version is for Excel 2003
I would welcome any feedback at the following email cjcruz[at]vtr.net

Available Tool-Files with User Developed Excel Functions
Available files for download

Some examples of these Visual Basic functions being applied:
Air and saturated water properties
Water properties
Circular channels
Slurries
Settling velocity and drag coefficient
Pipe dimension and friction factor
Radiation view factors

Examples of Piping Calculation Reports Using User Developed Functions
Piping Calculation Reports


You can leave your comments hear!

General Description

The spread sheets presented here, include all Excel functions required in each case. To produce an Excel add-in from an Excel function, save the Excel function as a complement. Prior to convert an Excel function to an Add-in, it is convenient to eliminate all sheets that do not contain information required (to be read) by the function. At least one sheet needs to be maintained, and it could be an empty one. Examples of functions that read information from a sheet are the "Pipe dimensions functions" and the "Air and water properties functions" It has to be considered, that it is not convenient that the same function is available twice. That could happen, for example, if two Excel books are opened and both contain the same function. Also it could happen that an Excel book has a certain function and at the same time this function has been installed and is available as an add-in function. In this case, the add-in function should be disabled.

See Recommended Good Practice and Disclaimer, at the end of the page.


Available tool-files for download

Air receivers volume calculation.xls
(This file presents the calculation of an air receiver, and shows several references related to this theme. Application example and derivation of equation to determine the receiver volume. Rev. 24.06.2014)

Atmospheric_temperature_pressure_and_density_as_function_of_the_height_above_sea_level.xls
(This file presents the calculation of atmospheric temperature, pressure and density as a function of the heigth above sea level, according 1976 U.S. Standard Atmosphere. It includes also an approximate method that can be applied for a range of heights 0 km.a.s.l. < H < 6 km.a.s.l. with an error less than 0.1% . Also, it is presented an equation to calculate the water vapor. pressure as a function of temperature. References included. Rev. 22.06.2014)

Average_particle_size_determination_d50_from_gravimetric_analysis_Mesh.xls. Rev. 22.09.2013
(For a given granulometric analysis (mesh size vs. Retained percentage) a table of "Mesh vs. Particle size (mesh opening)" is made. The plotted curve allows to find the particle size orresponding to a 50% retained percentage: This is the average particle size or d50 value. Evaluation of a filtrated sample propertiers. Gravimetric composition of a flow resulting from the joint of two flows. Rev. 31.01.2014)

Bernoulli and piezometric line.xls.
(Basic definitions and graphic Rev. 06.04.2014)

Bingham_slurries_pressure_drop_calculation.xls
(This file presents some calculation examples of Bingham fluids, from "Slurry Systems Handbook", Abulanga. In some cases the examples are solved using the function Slurry_Friction_Factor_Bingham_Re_He. Rev. 31.01.2014)

Blower_Air_line.xls
(This file presents a calculation sheet for an air line. The pressure drop in each fitting and pipe is calculated and the parameters in a new line are calculated based in the resulting pressure of the precedent line. Rev. 31.01.2014)

Channel. 0.- Channels and pipes with frictional and singular pressure drop.
(This file gives a resume channel properties for circular, semi-circular and rectangular channels. Deductions are included. Rev. 31.01.2014)

Channel. 1.- Circular channel. Array_output. Constant_Manning_coefficient.
(This file gives a matrix output of results for a circular channel with slurry as fluid. Rev. 31.01.2014)

Channel. 2.- Three channel types. Three_sizing_options. Constant_Manning_coefficient.
(This file is an application that allows the selection of the channel type and offers three size options. Rev. 31.01.2014)

Channel. 3.- Channels resume. Constant_Manning_coefficient. Comparison with Hcanales.
(This file gives a resume of channel functions and shows a comparison with results of "Hcanales". Rev. 31.01.2014)

Channel. 4.- Circular channel with. Constant Manning friction coefficient.
(This file is an application for circular channels with constant Manning coefficient. Rev. 31.01.2014)

Channel. 5.- Three channel types. Array_&_single_functions. Variable_Manning_coefficient.
(This file is an application with variable Manning coefficient. Is valid for the three channel types and gives single functions as well as an array of functions. Rev. 31.01.2014)

Compresor_power_and_air_discharge_ temperature.xls
(This file calculates the compressor power of an isentropic and of a real process. Also, the exit temperature of an isentropic and of a real process is calculated. Rev. 31.01.2014)

Concentration of nitrogen in a furnace as function of the number of volume changes.xls
(A furnace works in ambient of nitrogen. It is required to know the Number of Volume Changes to obtain a desired nitrogen concentration in the furnace. Rev. 18.07.2014)

Cooling_a_pipe_filled_with_water.xls
(This application calculates the cooling time of water in a carbon steel pipe. The theory needed is deducted. Calculation examples of pipes with and without insulation are presented. A comparison with the results presented in the Mechanical Insulation Design Guide (NMIC) is included. Rev. 31/01/2014)

Cooling tower. Application_ Treybal.xls
(This file is an applications of the Merkel theory for cooling towers. Some correction have been made, nomenclature reviewed and some literature added. Still some explanations to be included. Re. 08.11.2014)

Cooling tower. Merkel theory_Treybal.xls
(This file presents a resume of Merkel's theory for cooling tower, taken from Robert Treybal, Operaciones de transferencia de masa Rev. 31.01.2014)

Coupled water tanks. Stabilization time, oscilation amplitud.xls
(This file presents the solution of the system of differential equations, resulting from the water movement between two tanks. The problem is solved using a finite differences method. This file will part of a future section on finite differences applications. A mathematical criteria to define time acceptable some interval is required. Rev. 13.05.2014)

Detention_time_of_impulsion_system.xls
(The routine calculates the time interval "t", from the de-energization of the pump, until the system comes to rest. It is considered the inertia of the pump, motor and fluid and the friction between fluid and pipe. An ascending pipe with constant slope is assumed. The friction factor is considered constant and with the value of the steady state condition. Rev. 01.06.2014)

Dimensioning_compressed_air_installations_Atlas_Copco.xls
(This file uses an Atlas Copco reference for the dimensioning of a compressd air installation. It includes compressor, aftercooler, receiver, dryer and pressure drop. Rev. 31.01.2014)

Excel Functions. Part 1 (Eng).pps
(Tutorial for Excel functions)

Excel Functions. Part 2 (Eng).pps
(Tutorial for Excel functions)

Excel Functions. Part 3 (Eng).pps
(Tutorial for Excel functions)

Expansion_loop.xls
(This file derives the expansion loop calculation equation an presents a calculation example. Rev. 31.01.2014)

Flanges_Temperature_and_Pressure_Ratings_for_Group_1_1_materials.xls
(Maximum temperature and pressure ratings of flanges conforming dimensions ASME B16.5 Pipe Flanges and Flanged Fittings - and materials specification to ASTM A-105. Rev. 31.01.2014)

Friction_and_singular_pressure_drop.xls
(This file presents a routine for the calculation of pressure drops due to friction and singularities. Several functions are included for the calculation of fittings and valves. Rev. 03.08.2014)

Funciones_Excel_(Power_ point_spanish). Parte_1.pps
(Intrucción al uso de funciones Excel, Parte 1)

Funciones_Excel_(Power_ point_spanish). Parte_2.pps
(Intrucción al uso de funciones Excel, Parte 2)

Funciones_Excel_(Power_ point_spanish). Parte_3.pps
(Intrucción al uso de funciones Excel, Parte 3)

Gravitational_adduction_Water_ Hammer(Spanish).xls
(Minimum and maximum pressures developed in the dischatge line of a tank for the cases of quick and slow closing. Rev. 31.01.2014)

Gravitational_discharge_of_Slurry._Three_diameter options(Spanish).xls
(Gravitational discharge of slurry with the option of three pipe sizes, under consideration of three flow rates.. Rev. 31.01.2014)

Gravitational_discharge_of_water. Ground profile_vs_Piezometric_elevaton.xls
(Gravitational discharge through a pipe, for a given ground profile. Rev. 31.01.2014)

Heat loss from a buried oil pipe.xls
(Heat loss from an insulated and a uninsulated buried pipe. The shape form method is used. Rev. 23.02.2014)

Heat loss from an indoor pipe.xls
(Heat loss from an insulated indoor pipe. Heat is lost from the exterior pipe surface by convection to the ambient and by radiation interchange with surrounding surfaces. Rev. 09.07.2014)

Heat loss from an outdoor pipe.xls
(Heat loss from an insulated outdoor pipe. Heat is lost from the exterior pipe surface by convection to the ambient and by radiation interchange with a clear sky night. Rev. 09.07.2014)

Heat loss. Convection on a tube.xls
(Convection coefficients for outside and inside of a pipe. Natural, forced and combined outside coefficients and forced interior coefficient for steam as fluid. Rev. 09.07.2014)

Heat loss. Finned tubes. Heat flow_ U factor_ Fin efficiency.xls
(Heat flow from a finned pipe. Fin efficiency according Schneider. Incropera example. Rev. 09.07.2014)

Heat loss. U factor for resistances in series and in parallel.xls
(Global heat transfer coefficients "U" for several pipe arrangements. U factors referred to the inside and outside pipe surface. Rev. 09.07.2014)

Heat loss. Underwater pipe for effluent discharge.xls
(Underwater pipe for effluent discharge. Discharge temperature of effluent in the sea and heat flow rate from the pipe into the sea. Rev. 10.07.2014)

Heat transfer. Finite differences for a steady state system. Implicite and explicite methods. Incropera.xls
(Heat transfer by the finite differences method, for steady state systems, using the implicite and explicite methods. Examples and derivation of equations from Incropera. Rev. 22.07.2014)

Ideal gas law. Application to air.xls
(Application of ideal gas law to determine air density)

Limit_suction_height_and_Minimum_submergence.xls
(This file presents calculation routines for the suction limit height and minimum submergence of a water pump. Rev. 31.01.2014)

Line sizing criteria as per different international standards (Ajay S. Saypute).xls
(Information on standards for line sizing Rev. 31.01.2014)

Link to some free download & freeware thermodynamic and hydraulic files.xls
(Information on links for hydraulic and thermodynamic free information. Rev. 31.01.2014)

Link_to_get_the_Steamdat_functions.xls
(The file is available and free to use at http://www.afconsult.com Rev. 10.02.2014)

Manning_s_coefficient.xls
(Manning`s coefficient as a function of pipe diameter, absolute rugosity and Reynolds number. Rev. 31.01.2014)

Max-Allowable-Pressure-of-Pipes-and-Pipelines-CER-04022013-1 (V. S. Kumar-Unprotected).xls
( Information on maximum allowed pressures. Rev. 31.01.2014)

Mc_Elvain_Cave_Durand_Bingham_fluids_HR_value.xls
(This file presents functions for the calculation of two slurry correction factors applied to the deposition velocity: - Mc Elvain and Cave correction factor and Durand correction factor. (This two function are a digitalization of the curves and therefore no equation is used). - Also is presented a function for Weir - HR factor for estimating the head and the efficiency of slurries, based on the values for water (Note. Weir, in later publications, is proposing a "HR-value" determination method that also requires the impeller diameter as input data. Rev. 31.01.2014)

Minimum_distance_between_pipes_with_ flanches.xls
(Flanches dimensions according ASME B16.5-2003. Minimum distance between flanches and pipes 30 mm. Valid for pipes without insulation. Distances to be verified if lateral movements or expansions could occur and also if orifice plates or other elements are present. Verify that there is not an occurrence of two flanges face to face. Pipes according ASME B36.10M-1996. Rev. 31.01.2014)

Mollier_diagram.xls
(A Pressure-Enthalpy, mollier type diagram, is being built by means of Steamdat functions. Rev. 31.01.2014)

Moody_diagram.xls
(For 0 < Re < 2300 Laminar region. Hagen - Poiseuille equation. For 2300 =< Re =< 4000 Critical region. Churchill equation. For 4000 < Re Transition and turbulent regions. Colebrook equation. There is not a theory describing the critical region. Churchill equation describes relatively well this region, for smooth pipes with Rrel <= 0.01, giving conservative values, when compared with Nikuradse experimental data. Although Churchill equation describes also the transition and turbulente regions in accordance with Colebrook, this last equation is used in these regions because its use is often required in certain design criteria. Rev. 31.01.2014)

Normal_to_real_flow_rate_and_FAD_flow rate.xls
(This file presents routines to transform Normal to Real flow rates and inversely, Standard to real flow rates and inversely and FAD flow rates to real or Normal flow rates. Rev. 10.02.2014)

Number of Transfer Units 'NTU'. Condenser application.xls
(This file presents a basic condenser application with the use of the Number of Transfer Units Rev. 06.04.2014)

Orifice_Plates.xls
(This file presents routines to calculate orifices plates with applications for air and water. Also, Cameron eqautions for water are presented. Rev. 31.01.2014)

Pipe_dimensions_and_friction_factor.xls
(Pipe dimensions for carbon steel, stainless steel, HDPE PE100, HDPE PE80, Fibre reinforced polyethylene, pipe friction factor for Darcy-Weisbach equation and Manning's coefficient. Rev. 31.01.2014)

Pipe_maximum_alowable_pressures_for_A53_A106_and_API_5L.xls
(Maximum allowable pressure and temperature ratings for petroleum refinery piping and chemical plant piping systems according ANSI/ASME B31.3 (2008) Process piping, materials grade B: A53, A106, API 5L, pipes with plane ends. (Allowable stresses from ASME B31.3, 2008, page 146) Maximum pressure calculated according Ec. 3a. Rev. 31.01.2014)

Pipe_Wall_Thickness_Calculation_according_ASME_B31_3.xls
(Pipe dimensions for carbon steel, stainless steel, HDPE PE100, HDPE PE80, Fibre reinforced polyethylene, pipe friction factor for Darcy-Weisbach equation and Manning's coefficient. Rev. 31.01.2014)

Pressure drop calculation equations for PIPING and PIPELINE (Ajay S. Saypute).xls
(Equations for pressure drop calculation. Rev. 31.01.2014)

Pressure loss in a steam pipe.xls
(Frictional and singular pressure losses in a pipe with steam. Rev. 23.02.2014)

Pressure loss in valves with gas as a fluid. Normal and choked flow (SI).xls
(Equations and examples of gas flow in valves. Rev. 23.02.2014)

Pressure_rating_ for_PVC_pipes .xls
(Pressure rating for industrial PVC, schedules 40, 80 and 120. Rev. 31.01.2014)

Propane_Butane_Saturation_Properties.xls
(Propane and butane saturation properties, gas and liquids. Rev. 31.01.2014)

Psychrometric charts.xls
(Psychrometric charts: Dry and wet bulb temperature, absolute humidity, relative humidity, enthalpy, for heights above sea level of 0 m.a.s.l. and 5300 m.a.s.l. Rev. 31.01.2014)

Psychrometric functions_Resume.xls
(Psychrometric functions, only a resume: Dry and wet bulb temperature, absolute humidity, relative humidity, enthalpy, dew point temperature, specific volume and density, for heights above sea level til 5300 m.a.s.l. Rev. 23.02.2014)

Psychrometric functions_Deductions.xls
(Psychrometric functions: Dry and wet bulb temperature, absolute humidity, relative humidity, enthalpy, dew point temperature, specific volume and density, for heights above sea level til 5300 m.a.s.l. Rev. 31.01.2014)

Psychrometry. Heat recovery air handling unit (Ahu). By Ömer Faruk D.xls
(This spreadsheet calculates air flow and battery capacity for Air Handling Units. The data used corresponds to location in Turkey. In the example, data for the city of Bursa has been used. You can change the data according to your city, in the Data page. By Omer Faruk D., Makine Mühendisi , Mechanical Engineer Rev. 01.10.2014)

Pump power derivation for slurry with froth, according Weir .xls
(Derivation of equation for slurry froth pump according a Weir. Rev. 31.01.2014)

Pumps_Froth_Selection_Warman.xls
(A froth pump calculation according a Warman' reference. Ref. 31.01.2014)

Pump. Heterogeneous_Slurries_Type_A_Warman.xls
(A froth pump calculation for heterogeneous slurry, according a Warman' reference. Ref. 31.01.2014)

Pump. TDH , NPSH, Power_for water.xls
(Pumpinh system between two water tanks. Results arecalculated in a spreadsheet and by means of "user defined Excel functions" Pump selection using a free pump selection program). Ref. 09.09.2014)

Pumps_Slurry_Selection_Typical_Warman.xls
(A type slurries, according Weir clasification: Weight concentration 0 % <= Cw <= 40 % and average particle size 50 microns < d50 < 300 microns To calculate the pressure drop of a "Weir type A slurry", the system is to be calculated as if the fluid were water. The file presents a usual input data sheet a water pressure drop calculation and finaly the calculation of the pressure difference that in some cases has to be added to the calculated pressure. Rev.- 31.01.2014)

Reception of data from a matrix.xls
(Reception of matrix output data from a VB function in an Excel sheet as a vertical matrix. Rev. 31.01.2014)

Relationships_between_Cv_Kv_and_C.xls
(Determinaqtion of Darcy-Weisbach "K" factor as a function of "Cv" value from valves. Rev. 31.01.2014)

Sand_trap.xls
(Determination of the basic sand trap dimensions using the function Pipe_Slurry_Vel_Decantacion_d_rs_rL_mu. Rev. 31.01.2014)

Saturated_water_and_dry_air_properties.xls.
(Water and air properties as a function of temperature. Rev. 31.01.2014)

Settling_velocity_of_spherical_particles.xls
(Settling velocity of spherical particles as function of particle diameter, solids density, liquid density and liquid absolute viscosity. Function Particle_Settling_velocity_d_rs_rL_mu(d, rs,rL,mu). Function Particle drag coefficient CD as function of particle Reynolds number. Function Particle_Drag_Coefficient_CD_Re. Rev. 31.01.2014)

Shperical_particle_drag_coefficient.xls
(Shperical particle drag coefficient as a function of particle Reynolds number. Rev. 31.01.2014)

Slope_required_for_a_pipe_to_avoid_fluid_accumulation.xls
(Slope of a pipe to allow it to be emptied. Rev. 31.01.2014)

Slurry properties.xls
(Relations between slury concentrations, densities and specific weights. Rev. 31.01.2014)

Slurry_settling_velocity_according_JRI.xls
(JRI recommend thre types of equations to calculated deposition velocities, according the particle average size and pipe diameter. Rev. 31.01.2014)

Sound_pressure_level.xls
(Calculation of SPL, based on octave band test data. Rev. 31.01.2014)

Steam_flow_required_in_a_pulp_dryer.xls
(Determination of steam requirements for a vapor driven slurry dryer. Steam and condensate pipes are defined. Rev. 31.01.2014)

Steamdat_applications.xls
(Steamdat function used to calculate a steam turbine stage and pressure reducing valve "PRV" with desuperheating. Rev. 31.01.2014)

Stress_Young_Modulus_and_Thermal_Expansion_coefficients_of_steels.xls
(Steel properties as a function of the temperature. Rev. 31.01.2014)

Tailings deposition_by Gordon McPhail_2008.pdf
(Prediction of the beach profile of high density thickened tailings from rheological and small scale trial deposition data. By Gordon McPhail, from Metago Environmental Engineers. Rev. 13.10.2014)

Tank sulfuric acid storage. API 650-1998. (Spanish).xls
(Calculation report for a sulfuric acid tank. Rev. 31.01.2014)

Tank_venting_according_API_2000.xls
(Determination of tank venting diameter, according API 2000)

Valves_and_fittings_pressure_drop_coefficients.xls
(Functions for valves: Ball, Butterfly, Knife, Globe, Pinch, Diaphragm, Plug, Check.xls Fittings: Y_strainer, enlargements and reductions. Rev. 10.02.2014)

Viscosity_of_oils_as_a_function_of_temperature.xls
(The viscosity of oils can be shown as straight lines in a Log-Nat Diagram This concept is applied to the case of Rimula 15W-40 oil, where a paire of points "viscosity - temperature" are known. Rev. 31.01.2014)

Viscosity_ratio_of_slurries.xls
(Slurry viscosity ratio according Einstein, Thomas and Wellman. Rev. 31.01.2014)

Volumetric flow rate required by an actuator and average volumetric flow required by the network.xls
(This file is developed as a help when designing air nets. The consumer points require an "instantaneous flow rate", defined by the installed equipment, for the duration of each operation. On the other hand, the main pipes should be designed for the probable maximum flow (PMF). Rev. 31.01.2014)

Water_ hammer_damper_tank_Hydropack example.xls
( Selection of a water_ hammer_damper_tank according Hydropack. Rev. 31.01.2014)

Water_and_slurry_hammer.xls
( Water hammer examples: Tyler. Water hammer in a carbon steel pipe Pehmco: Water hammer in a HDPE pipe Tsingua University: Slurry hammer in a HDPE PE80 pipe. Rev. 31.01.2014)

Water hammer. Method of characteristics. Theory .xls
( The Method of Characteristics transform the system of PDE in a system of Total Differential Equations (TDE). The system of TDE can be solved numerically by different mathematical methods. The application is based on a Streeter example. Rev. 24.05.2014)

Water hammer example solved by the method of characteristics, Using Visual Basic and Finite Differences.xls
( An application for a simple case consisting in a reservoir, a horizontal pipe and a valve. The water hammer problem is solved by Finite Differences and also using Visual Basic. An application example is solved with input data from a Streeter example. Results of the solution by finite differences and V.B. are in agreement with the results from Streeter example. Rev. 16.12.2014)

Standard Piping Calculation Reports

Pump. Demineralized water(Spanish).xls
(Standard type calculation for water. Rev. 31.01.2014)

Pump. Fuel oil(Spanish).xls
( Standard type calculation for oil circuit. Rev. 31.01.2014)

Pump. Lubricating oil(Spanish).xls
(Standard type calculation for lubticating oil circuit. Rev. 31.01.2014)

Pump. Reactives(Spanish).xls
(Standard type calculation for lubticating oil circuit. Rev. 31.01.2014)

Pump. Slurry froth.Three diameter options (Rev. 24.10.2013).xls
(Pump selection for Slurry with froth, according Weir. Rev. 31.01.2014)

Pump. Slurry lime_Loop(Spanish).xls
(Standard type calculation for lubticating oil circuit. Rev. 31.01.2014)

Pump. Water_circuit system_Primary_Grinding_dust_suppression(Spanish).xls
(Standard type calculation for a water net. Rev. 31.01.2014)

Water_hammer_calculation_of gravitational_adduction.xls
( Waterhammer calculation for a gravitational line. Rev. 31.01.2014)

Some Examples of Piping Tools Applications

Air and saturated water properties as a function of temperature [ºC]


xls file with the use of air and saturated water functions



Water properties (Vapor and liquid)

A series of thermodynamic functions, from Lennart Delin and Johan Nygaard
Senior Consultants, ÅF-Process
Visiting address: Fleminggatan 7 | Delivery: Box 8309, SE-104 20 Stockholm
Direct: +46 (0)10 505 12 78 | Fax: +46 (0)10 505  27 57 | Mobile: +46 (0)70 342 12 78
e-mail: lennart.delin@afconsult.com | http://www.afconsult.com
Mollier diagram file
Address to download Steamdat
information file for Steamdat



Circular channels

Open channels with circular section
xls file for the flow of water in circular channels
xls file for the flow of slurry in circular channels

xls file for flow in circular, semicircular channels and rectangular channels.





Slurries

Slurry properties
xls file for the calculation of slurry properties.



Settling velocity and drag coefficient

Spherical particles settling velocity and drag coefficient
xls file for the calculation of settling velocity
Shperical particle drag coefficient"
Application to a "sand trap"



Pipe dimension and friction factor

Exterior and interior diameters, and thickness of different pipe materials. Determination of the friction factor
81.- Pipe dimensions and friction factor functions.xls
82.- Moody diagram.xls





Radiation view factors

Radiation view factors for parallel oposite and perpendicular rectangles with a common adge,
as a function of its geometric parameters.
Applications of radiation view factors
Application to the radiation interchange among the walls of a furnace
Download of J.R. Howell view factors catalog



I welcome any comments or you can contact me by writing to cjcruz[@]vtr.net or cjcruz[@]piping-tools.net.
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RECOMMENDED GOOD PRACTICE

The files are free of any virus. As general good practice, it is recommended to check any type of file to be free of virus before using them. The presented files contain Excel functions and it is known that Excel has some problems in recognizing clean files. For this reason it is recommended that, once a file has been checked for viruses and has been recognized as a clean file, to put it in a directory declared as a trusted directory. To declare a directory or a file as a safe document, use the Excel trust Center. This providence will avoid that under given circumstances Excel will erase the Visual Basic code.

DISCLAIMER

The author shall not be responsible for losses of any kind resulting from use of this program or of any documentation and can in no way provide compensation for any losses sustained including but not limited to any obligation, liability, right or remedy for tort nor any business expense, machine downtime or damage caused to the user by any deficiency, defect or error in the program or in any such documentation or any malfunction of the program or for any incidental or consequential losses, damages, or costs, however caused.

 

 

 
   

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   Creative Commons License   This work is published under a license Creative Commons.